phase speed

Earlier this year at Forscherfreizeit Ratzeburg – the summer camp at which Conny, Siska, Martin, a bunch of teenagers and myself spent a week sailing, exploring and playing with water – I spent a good amount of time staring at waves hitting the wooden boards that form the slip in the port. They create a nice slope with a very interesting structure, especially at the joints where the angle of the slope isn’t exactly the same.

Watch what happens when the wave approaches the shore (and focus on the left part of the picture, where it is clearer):

At first, it arrives pretty much as an ordinary wave.

As it is running up the slip, you start seeing the structure of the boards below.

As the wave becomes steeper and steeper, the front one is being slowed down more than the second one, because it is in shallower water (and we all know that the phase velocity of shallow water waves depends on the water depth, right?).

We are so used to seeing waves behave in a certain way that we usually don’t stop and think about why waves behave the way they behave.

Imagine a headland with not-very-steep slopes, and wave crests approaching it. Consider now two possible scenarios. In the first one, the wave crests bend around the headland almost as to embrace it. In the second one, wave crests bend away to channel the energy through the deeper waters around it. Which one will it be?

The only difference between those scenarios is that in one case waves are being refracted towards regions of lower velocities and in the other towards regions of higher velocities.